Digitization Noise in Power Spectral Analysis

Abstract

It is well-known that the digitization noise variance is ?2/12 for a continuous time series sampled with the signal resolution ?. It is also generally accepted that this variance often has a white-power spectral density. We have examined in detail under which circumstances this is the case for turbulent media and found that for a joint Gaussian signal x(t) with variance σ2{x} and a Taylor microscale ? the digitization noise is indeed white if (?t/?)(σ{x}/?) ? t, where ?t is the constant sampling time. Otherwise, the digitization noise tends to be concentrated at lower frequencies. White spectral noise with known variance is easily removed, so from a practical point of view ?t should not be too small.